Problem: In the right triangle shown, $AC = 3$ and $AB = 9$. What is $BC$ ? $A$ $C$ $B$ $3$ $?$ $9$
Answer: We know $a^2 + b^2 = c^2$ We want to find $a$ ; let $b = 3$ and $c = 9$ So $a^2 = c^2 - b^2 = 9^2 - 3^2 = 72$ Then, $a = \sqrt{72}$ Simplifying the radical gives $a = 6\sqrt{2}.$